A057517 Binary encodings of the Catalan mountain ranges with exactly one sea-level valley, i.e., the rooted plane trees with root degree = 2.

10, 44, 50, 180, 184, 204, 210, 226, 724, 728, 740, 744, 752, 820, 824, 844, 850, 866, 908, 914, 930, 962, 2900, 2904, 2916, 2920, 2928, 2964, 2968, 2980, 2984, 2992, 3012, 3016, 3024, 3040, 3284, 3288, 3300, 3304, 3312, 3380, 3384, 3404, 3410, 3426

Offset: 1

Author

Antti Karttunen, Sep 03 2000

Keywords

• nonn

Comments

This bijective mapping from all rooted plane trees to one node larger, root degree = 2 trees illustrates the fact that CONV(A000108, A000108) = LEFT(A000108). (Catalan numbers shift left under convolution).

Crossrefs

Cf. A057501 (for binexp2pars, pars2binexp, car, cdr), A057518, A057519, A057122. Single-trunked trees: A057547.

Programs

Maple

alltrees2doubletrunked := n -> pars2binexp(alltrees2doubletrunkedP(binexp2pars(n)));
alltrees2doubletrunkedP := h -> [car(h),cdr(h)];

Formula

a(n) = alltrees2doubletrunked(A014486(n)) (Starting from n=1).